How to find parameters of the following coefficient based on optimization tool?

Hi everyone, I have the following input and function, my purpose is to calculate the value of a,m and n which are scalars using curve fitting in matlab. I have:

ew=[0.679 0.613 0.613 0.501 0.497 0.50 0.389 0.386 0.386 0.391 0.390 0.288 0.288 0.288 0.289 0.289]; Hw=[0.757 0.669 0.71 0.577 0.57 0.60 0.50 0.55 0.52 0.50 0.476 0.353 0.388 0.379 0.431 0.371]; k=[0.217 0.217 0.217 0.163 0.163 0.163 0.131 0.131 0.131 0.131 0.131 0.109 0.109 0.109 0.109 0.109];

Hw=[ew*(1+0.36(1-ew))]*C; C=exp[-a*(k^m)*(1-ew)^n];

any help would be appreciated.

[Alan Weiss]

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Alan Weiss

MATLAB mathematical toolbox documentation

Answer 1

[Roger Stafford]

Define the following sum of squares of differences:

   ew=[0.679 0.613 0.613 0.501 0.497 0.50  0.389 0.386 0.386 0.391 0.390 0.288 0.288 0.288 0.289 0.289]; 
   Hw=[0.757 0.669 0.71  0.577 0.57  0.60  0.50  0.55  0.52  0.50  0.476 0.353 0.388 0.379 0.431 0.371]; 
   k= [0.217 0.217 0.217 0.163 0.163 0.163 0.131 0.131 0.131 0.131 0.131 0.109 0.109 0.109 0.109 0.109];
   function s = myfun(a,m,n)
     s = sum((Hw-ew.*(1+0.36(1-ew)).*exp[-a*(k.^m).*(1-ew).^n)).^2);
   return

and then use that subfunction for optimization of a, m, and n using 'fminsearch' or 'fminunc'. Their descriptions can be found at:

   http://www.mathworks.com/help/matlab/ref/fminsearch.html
   http://www.mathworks.com/help/optim/ug/fminunc.html

Answer 2

[Parham Babakhani Dehkordi]

Thank you Roger for your help,but I still have a problem to get a solution, I arranged my code with initial guesses for a=0.31,m=1 and n=0.7 and also I considered a=x(1), m=x(2) and n=x(3) as follows:

for i=1:16
x =fminsearch(@(x) (Hw(i)-(ew(i)*(1+0.36*(1-ew(i)))))*exp(-x(1)*k(i)^x(2)*(1-ew(i))^x(3)), [0.31 1.0 0.7])
end

there is an error which says Error: File: fminsearch.m Line: 31 Column: 5
Function definitions are not permitted in this context.

Actually I could not properly use handle function directly to pass it through function function (in this case fminsearch). Sorry Alan, I am new user to Matlab.